Method and apparatus for weighted non-binary repeat accumulate coding and space-time coding

ABSTRACT

An apparatus and method for weighted non-binary RA coding and space-time coding are disclosed. Transmission data is divided in the units of frames each having mN bits, and each frame is further segmented into N blocks, each block containing m bits. The N blocks are converted to N non-binary GF(2 m ) elements. These N non-binary symbols are repeated by a repetition factor r. The rN symbols are multiplied by weighting factors being GF(2 m ) elements other than zero. The rN weighted symbols are interleaved and accumulated. The rN accumulated symbols are transmitted to a receiver, or each of the rN accumulated symbols is demapped to m bits prior to transmission. Therefore, information can be transmitted reliably in a wireless communication system.

PRIORITY

[0001] This application claims priority under 35 U.S.C. § 119 to anapplication entitled “Method and Apparatus for Weighted Non-BinaryRepeat Accumulate Coding and Space-Time Coding” filed in the KoreanIndustrial Property Office on Jan. 16, 2002 and assigned Ser. No.2002-2414, the contents of which are hereby incorporated herein byreference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates generally to a channel coder and achannel coding method in a mobile communication system using multipleantennas for efficiently correcting errors in a channel at a receiver,and in particular, to an apparatus and method for error correctioncoding that helps detection and correction of errors in a channel withhigh reliability in a wireless communications system.

[0004] 2. Description of the Related Art

[0005] In a mobile communication system, a transmitter adds acorresponding parity data stream to information data so that a receivercan receive the information data correctly. This coding technique can beimplemented in different coders in the transmitter: a Reed-Solomoncoder, a convolutional coder, a turbo coder, and a concatenatedReed-Solomon and convolutional coder. The concatenated coder comprisestwo constituent coders and an interleaver that connects them.

[0006]FIG. 1 is a block diagram of a typical turbo coder. Referring toFIG. 1, the turbo coder includes a first constituent coder 100, a turbointerleaver 102, a second constituent coder 104, and a multiplexer (MUX)106. In operation, an input frame data stream is simply output to theMUX 106 and fed to both the first constituent coder 100 and the turbointerleaver 102. The first constituent coder 100 encodes the frame datastream and the turbo interleaver 102 interleaves it. The secondconstituent coder 104 encodes the interleaved data. The MUX 106multiplexes the input frame data stream and the data received from thefirst and second constituent coders 100 and 104. Here, the turbointerleaver 102 permutes the sequence of the information bits of theframe data stream and generates interleaver addresses according to itsinterleaver size. This turbo interleaver 102 functions to maximize turbocoding performance.

[0007] As illustrated in FIG. 1, for the input of one input frame datastream, the turbo coder with a code rate of ⅓ outputs three frame datastreams, which are the input frame data stream and two parity frame datastreams for correcting the input frame data stream.

[0008] If received frame data streams have a full rank, excellent errorcorrection performance can be achieved at a receiver. Hereinbelow, rankwill first be described.

[0009] Let the input frame data stream be [1 1 0] and the turbo coderoutput be $\quad\begin{pmatrix}1 & 1 & 0 \\1 & 0 & 1 \\0 & 1 & 1\end{pmatrix}$

[0010] That is, the first constituent coder 100 outputs [1 0 1] and thesecond constituent coder 104 outputs [0 1 1]. A rank is determined usingthe sum of the other columns or the subtraction between the othercolumns excepting a particular column in the matrix. The third column ofthe above matrix can be represented as the sum of the first and secondcolumns. Excepting the third column, there remain two columns. Thus therank of the output frame data stream is 2. A full rank is defined whereit is impossible to represent a particular column as the sum of theother columns or the subtraction between the other columns. A full-rankmodel is given below.

[0011] output frame data stream: $\quad\begin{pmatrix}1 & 1 & 1 \\1 & 0 & 1 \\0 & 1 & 1\end{pmatrix}$

[0012] When coding using binary codes, the output frame data stream isgenerally of a full rank. However, it is not of a full rank ifnon-binary codes are used. That is, a non-binary coder, which repeats aninput frame data stream a predetermined number of times, outputs a framedata stream in a matrix where a particular column can be represented asthe sum of the other columns or the difference between the othercolumns. Thus, it is difficult to recover the original frame data streamusing the received frame data stream at the receiver. Accordingly, thereis a need for a full-rank error correction coder using non-binary codes.

SUMMARY OF THE INVENTION

[0013] It is, therefore, an object of the present invention to provide anon-binary repeat accumulate (RA) coder having a full rank and a codingmethod thereof.

[0014] It is another object of the present invention to provide an errorcorrection coder and an error correction coding method using a full-ranknon-binary RA (Repeat-Accumulate) coder, which offer high reliability byenabling a receiver to recover a received data stream correctly in awireless communications system.

[0015] It is a further object of the present invention to provide aspace-time coder and a space-time coding method that achieve unity datarate and maximum antenna diversity in a wireless communications system.

[0016] To achieve the above and other objects, transmission data isdivided in the units of frames each having mN bits, and each frame isfurther segmented into N blocks, each block containing m bits. The Nblocks are converted to N non-binary GF(2^(m)) elements. These Nnon-binary symbols are repeated by a repetition factor r. The rN symbolsare multiplied by weighting factors being GF(2^(m)) elements other thanzero. The rN weighted symbols are interleaved and accumulated. The rNaccumulated symbols are transmitted to a receiver, or each of the rNaccumulated symbols is mapped to m binary bits prior to transmission.Therefore, information can be transmitted reliably in a wirelesscommunication system.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and other objects, features and advantages of thepresent invention will become more apparent from the following detaileddescription when taken in conjunction with the accompanying drawings inwhich:

[0018]FIG. 1 is a block diagram of a typical turbo coder;

[0019]FIG. 2 is a block diagram of an RA coder according to the presentinvention;

[0020]FIG. 3 is a block diagram of an embodiment of a space-time coderaccording to the present invention;

[0021]FIG. 4 is a block diagram of another embodiment of the space-timecoder according to the present invention; and

[0022]FIG. 5 is a block diagram of a third embodiment of the space-timecoder according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] Preferred embodiments of the present invention will be describedherein below with reference to the accompanying drawings. In thefollowing description, well-known functions or constructions are notdescribed in detail where they are well-known in the art.

[0024] Gaussian Approximation is useful for evaluation of theperformance of a coder using a Sum-Product decoding algorithm such as RAcodes or low-density parity check (LDPC) codes (see S. Y. Chung, T. J.Richardson, and L. Urbanke, Analysis of Sum-Product Decoding ofLow-Density Parity-Check Codes Using a Gaussian Approximation, IEEETrans. Inform. Theory, vol. 47, pp. 657-670, Feb. 2001). For GaussianApproximation, non-binary codes are represented as binary codes. Thenon-binary code symbols can be elements of a finite field, especiallyelements of a Galois Field GF(2^(m)) and the correlation between thebinary code symbols and the non-binary code symbols is based on thefinite field theory. This will be apparent in embodiments of the presentinvention. When the non-binary code symbols are represented as binarycode symbols to improve the performance of RA codes using theSum-Product decoding algorithm, repeated code symbols have regularityand thus repeated symbols in a parity check matrix for the Sum-Productdecoding algorithm are independent of each other. Therefore, in the caseof non-binary RA codes, the simple repetition degrades the performanceof the Sum-Product decoding algorithm. The independence of the binarycode symbols in the parity check matrix can be avoided by achieving adifferent representation of the repeated code symbols. The simplest,most efficient way is to use a weighter. The weighter increases thecorrelation between repeated symbols by randomizing output of theweighter. As a result, when the Sum-Product decoding algorithm is usedat a decoder, decoding performance is increased.

[0025]FIG. 2 is a block diagram of a non-binary RA coder according tothe present invention. Referring to FIG. 2, the non-binary RA codercomprises a mapper 200, a repeater 202, a weighter 204, an interleaver206, a coder 208, and a demapper 214. The mapper 200 receives N blocks,each block including m bits, that is, total number of input bits ismN-bit. This frame is a binary representation of transmission data. Themapper 200 converts the input binary bit stream to a non-binary bitstream. While the mapper 200 can be implemented in many ways, it usesthe Galois Field (GF) in the present invention. Yet, it is obviously tobe understood that a binary-non-binary mapping method is not confined tothe GF-based method.

[0026] If m is 3, the input frame can be expressed as a binary bitstream u₀, u₁, U₂, . . . , u_(3N) _(⁻) ₁. The mapper 200 maps 3 N bitsto N symbols, that is, maps an i^(th) block (i=0 to (3N⁻1)/3) having 3bits, (u_(3i), u_(3i+1), u_(3i+2)) to an element of GF(2³), U_(i). TheGF(2³) element, U_(i) corresponding to 3 bits is called a symbol. Table1 illustrates mapping of binary bits to non-binary bits in the GF(2³).TABLE 1 u_(3i), u_(3i+1), u_(3i+2) Addition Multiplication 000 0 0 100 11 = a⁷ 010 a a 110 1 + a a³ 001 a² a² 101 1 + a² a⁶ 011 a + a² a⁴ 1111 + a + a² a⁵

[0027] As illustrated in Table 1, although the mapper 200 maps inputblocks to non-binary symbols by GF addition (vector representation) orGF multiplication, the present invention will be described in thecontext of the GF addition.

[0028] The GF addition representation of binary bits equivalent to theirGF multiplication representation will be described below. A generatorpolynomial of non-binary codes over GF(2³) in a mobile communicationsystem is defined as

f(x)=x ³ +x+1   (1)

[0029] where f(x) is a primitive polynomial over GF(2³) and if a is aprimitive element of GF(2³), the following Eq. (2) is satisfied

f(a)=0   (2)

[0030] Thus the generator polynomial is a³+a+1=0 (i.e., a³=a+1). Anarbitrary symbol can be expressed as a linear combination of 1, a, anda². For a⁴(0 1 1),

a ⁴ =aa ³ =a(a+1)=a ² +a

[0031] In this manner, the GF addition representation of binary bits canbe derived from their GF multiplication representation, as illustratedin Table 1. As stated before, a 3-bit block (u_(3i), u_(3i+1), u_(3i+2))is converted to an element of GF(2³), U_(i) being a non-binary symbol.For the input of N 3-bit binary blocks, the mapper 200 outputs symbolsU₀, U₁, U₂, . . . , U_(N) _(⁻) ₁. A set of the output symbols is calledan element sequence.

[0032] These N symbols are provided to the repeater 202. A repetitionfactor is determined according to a data rate. If the repetition factoris r, the data rate is r/m (where m is the number of binary bits peroutput symbol U and is equal to the number of the transmit antennas). Toobtain a maximum data rate, r is set to m(r=m). For example, if m is 3,r is 3.

[0033] Thus, the repeater 202 repeats the input non-binary symbols U₀,U₁, U₂, . ., U_(N) _(⁻) ₁ three times and thus outputs non-binarysymbols X₀, X₁, X₂, . . . , X_(3N) _(⁻) ₁, which are expressed as

X _(3i) =X _(3i+1) =X _(3i+2) =U _(i) i=0,1,2, . . . N−1   (3)

[0034] Since for the input of one non-binary symbol, the repeater 202outputs three identical non-binary symbols as illustrated in Eq. (3),they are not of a full rank. To realize the full rank, X₀, X₁, X₂, . . ., X_(3N) _(⁻) ₁ are provided to the weighter 204.

[0035] The weighter 204 multiplies an i^(th) input non-binary symbol bya weighting factor ^(β) _(i) being a GF(2³) element. In an embodiment ofthe present invention, the number of weighting factors used in theweighter 204 is equal to the repetition factor r and weighting factorsare not zero. Specifically, the weighter 204 multiplies three identicalnon-binary symbols received from the repeater 202 by three differentweighting factors, respectively. While the GF is used here, it is a mereexemplary application. Thus, any weighting factors can be used as far asweighting the repeated non-binary symbols with the weighting factorsresults in a full rank. If the weighted non-binary symbols are Y₀, Y₁,Y₂, . . . , Y_(3N) _(⁻) ₁,

Y _(i)β_(i) X _(i) i=0,1,2, . . . , 3N−1

[0036] The interleaver 206 interleaves Y₀, Y₁, Y₂, . . . , Y_(3N) _(⁻) ₁on a symbol basis and outputs interleaved symbols Z₀, Z₁, Z₂, . . . ,Z_(3N) _(⁻) ₁ to the constituent coder 208. The interleaver 206functions to permute the sequence of the received symbols.

[0037] The coder 208 is an accumulator comprising an adder 210 and aregister 212, but a one-tap or two-tap RSC (Recursive SystematicConvolutional) coder can substitute for them. For the input of theinterleaver output Z₀, Z₁, Z₂, Z_(3N) _(⁻) ₁, the coder 208 outputs C₀,C₁, C₂, . . . , C_(3N) _(⁻) ₁. $\begin{matrix}{{C_{i} = {{\sum\limits_{j = 0}^{i}\quad {Z_{j}\quad i}} = 0}},1,2,\ldots \quad,{{3N} - 1}} & (5)\end{matrix}$

[0038] The demapper 214 demaps each of the non-binary symbols C₀, C₁,C₂, . . . , C_(3N) _(⁻) ₁ received from the coder 208 to a plurality ofbinary bits. Since the demapper 214 operates in the order reverse to themapping in the mapper 200, it converts each non-binary symbol over theGF(2³) to 3 binary bits. If the mapper 200 operates differently, thedemapper 214 also operates correspondingly. The demapper 214 maps anelement of GF(2³), C_(i) to a binary symbol (c_(i1), c_(i2), c_(i3)).The demapper output is transmitted to a receiver through an antenna.

[0039]FIGS. 3, 4 and 5 illustrate embodiments of a space-time coder withhigh reliability, which is realized by combining a plurality oftransmission/reception antennas and error correction techniques with thenon-binary RA coder illustrated in FIG. 2 according to the presentinvention.

[0040]FIG. 3 is a block diagram of an embodiment of the space-time coderusing BPSK (Binary Phase Shift Keying) according to the presentinvention. The pace-time coder is configured by adding a signal mapper(or bit distributor) 312 and a plurality of antennas 314, 316 and 318 tothe structure of the RA coder illustrated in FIG. 2. The functionalblocks from a mapper 300 to a demapper 310 operate in the same manner asthose from the mapper 200 to the demapper 214 illustrated in FIG. 2.Thus, their operations will not be described here.

[0041] The demapper 310 outputs a three-bit binary symbol (C_(i1),C_(i2), C_(i3)) to the signal mapper 312. The signal mapper (or bitdistributor) 312 maps the input bits (C_(i1), C_(i2), C_(i3)) to aBPSK-modulated signal (s_(i1), s_(i2), s_(i3)). BPSK is a scheme ofmodulating data using the phase of a carrier having a predeterminedamplitude and frequency. The BPSK-modulated signal (s_(i1), s_(i2),s_(i3)) is transmitted to the receiver through the antennas 314, 316 and318. The number of the antennas 314, 316 and 318 is related to that ofbits mapping to one non-binary symbol output from the demapper 3 10. Inthe present invention, since the bit symbol has three bits, threeantennas are used to thereby achieve high diversity performance. Asdescribed before, the data rate r/m can be up to 1. During an i^(th)time period, the signals s_(i1), s_(i2) and s_(i3) are transmittedthrough the antennas 314, 316 and 318, respectively.

[0042]FIG. 4 is a block diagram of another embodiment of the space-timecoder according to the present invention. Referring to FIG. 4, thetransmitter divides transmission data into frames, each frame containingmnN bits. Each mnN-bit frame is further segmented into nN m-bit blocks,where n is the number of sub-frames. A mapper 400 maps the nN blocks tonon-binary symbols in the same manner as the mapper 200 illustrated inFIG. 2.

[0043] A serial-to-parallel converter (SPC) 300 converts the non-binarynN symbol blocks to n sub-frames, each sub-frame having N blocks. If then sub-frames are expressed as U⁽¹⁾, U⁽²⁾, . . . , U^((n)), a k^(th)sub-frame contains N blocks U₀^((k)), U₁^((k)), …  , U_(N − 1)^((k)).

[0044] The k^(th) sub-frame U^((k)) is applied to the input of a k^(th)STC (Space Time code) block by SPC 410.

[0045] For the input of the k^(th) sub-frame U^((k)), the k^(th) STC(Space Time code) block outputs non-binary symbols C^((k)) through arepeater with a repetition factor r(^(≦)m), a weighter, an interleaver,and a coder. To obtain a maximum data rate, r=m. Repeaters 420 to 424,weighters 430 to 434, interleavers 440 to 444, coders 450 to 453, anddemappers 460 to 464 each perform the same operations as theircounterparts illustrated in FIG. 2, and the n STC (Space Time code)blocks have the same components. C^((k)) contains rN non-binary symbolsC₀^((k)), C₁^((k)), …  , C_(r  N − 1)^((k)).

[0046] Therefore, one sub-frame has rN non-binary symbols. A demapperconverts each of the rN non-binary symbols to corresponding m bits. Thatis, the demapper converts an i^(th) non-binary symbol in the k^(th) STC(Space Time code) block, C_(i)^((k))

[0047] being an element of GF(2^(m)), to m bits,c_(i1)^((k)), c_(i2)^((k)), …  , c_(i  m)^((k)).

[0048] The bit symbols output from the demappers 460 to 464 are providedto a signal mapper 470. The signal mapper 470 determines a signal s_(ij)to be transmitted through a j^(th) antenna at an i^(th) time using asignal constellation with a set of n bits received from the n demappersc_(i  j)⁽¹⁾, c_(i  j)⁽²⁾, …  , c_(i  j)^((n)).

[0049] The signal constellation is determined according to n. If n is 2,the signal constellation can be of QPSK (Quadrature Phase-Shift Keying).If n is 3, the signal constellation can be of 8QAM (Quadrature AmplitudeModulation). A signal transmitted through a j^(th) antenna is s_(0j),s_(1j). . . , s_(rN−1j) where 0 to r indicate transmission time. Thenumber of the transmission antennas 480 to 484 is equal to therepetition factor.

[0050]FIG. 5 is a block diagram of a third embodiment of the space-timecoder using m antennas according to the present invention. Referring toFIG. 5, the transmitter divides transmission data into frames, eachframe containing 2 mnN bits. Each 2 mnN-bit frame is further segmentedinto 2 nN m-bit blocks. A mapper 500 maps the 2 nN blocks to non-binarysymbols in the same manner as the mapper 200 illustrated in FIG. 2.

[0051] An SPC 510 converts the non-binary 2 nN symbol blocks to 2 nsub-frames, each sub-frame having N blocks. If the 2 n sub-frames areexpressed as U⁽¹⁾, U⁽²⁾, . . . , U^((2n)), a k^(th) sub-frame contains Nblocks U₀^((k)), U₁^((k)), …  , U_(N − 1)^((k)).

[0052] The k^(th) sub-frame U^((k)) is applied to the input of a k^(th)STC (Space Time code) block by SPC 510.

[0053] For the input of the k^(th) sub-frame U^((k)), the k^(th) STC(Space Time code) block outputs non-binary symbols Z^((k)) through arepeater with a repetition factor r(^(≦)m), a weighter, an interleaver,and a coder. To obtain a maximum data rate, r=m. Repeaters 520 to 526,weighters 530 to 536, interleavers 540 to 546, coders 550 to 556 anddemappers 560 to 566 comprising 2n STC (Space Time code) blocks eachperform the same operations as their counterparts illustrated in FIG. 2,and the 2n STC (Space Time code) blocks have the same components.Z^((k)) contains rN non-binary symbolsZ₀^((k)), Z₁^((k)), …  , Z_(r  N − 1)^((k)).

[0054] A demapper converts each of the rN non-binary symbols to a binarysymbol having m bits. That is, the demapper converts an i^(th)non-binary symbol in the k^(th) STC (Space Time code) block, Z_(i)^((k))

[0055] to m bits, Z_(i1)^((k)), Z_(i2)^((k)),  …  , Z_(im)^((k)).

[0056] The bit symbols z⁽¹⁾, z⁽²⁾, . . . , z^((n)) output from thedemappers 550 to 552 are provided to a first converter 560 , and the bitsymbols z^((n+1)), z^((n+2)), . . . , z^((2n)) output from the demappers554 to 556 are provided to a second converter 562. The first converter560 converts the received bit symbols to real-part symbolsY₀^(R), Y₁^(R),  …  , Y_(rN − 1)^(R)

[0057] by modulo 2 by the input integers. The second converter 562converts the received bit symbols to imaginary-part symbolsY₀^(I), Y₁^(I),  …  , Y_(rN − 1)^(I)

[0058] by modulo 2^(n) by the input integers. Thus, the converters 560and 562 function to convert input n bits to one signal. i^(th) signalsY_(i) ^(R) and Y_(i) ¹ output from the converters 560 and 562 can beexpressed as $\begin{matrix}{{{( {Y_{i1}^{R},Y_{i2}^{R},\quad \ldots \quad,Y_{im}^{R}} )\quad {and}\quad ( {Y_{i1}^{I},Y_{i2}^{I},\quad \ldots \quad,Y_{im}^{I}} )},{{which}\quad {are}}}{Y_{ij}^{R} = {z_{i\quad j}^{(1)} + {2z_{i\quad j}^{(2)}} + \ldots + {2^{n - I}z_{i\quad j}^{(n)}}}}} & (6) \\{Y_{ij}^{I} = {z_{i\quad j}^{({n + 1})} + {2z_{i\quad j}^{({n + 2})}} + \ldots + {2^{n - I}z_{i\quad j}^{({2n})}}}} & (7)\end{matrix}$

[0059] A first accumulator 570 accumulates the real-part symbolsY₀^(R), Y₁^(R),  …  , Y_(rN − 1)^(R)

[0060] and outputs a real-part sequenceC₀^(R), C₁^(R),  …  , C_(rN − 1)^(R)

[0061] and a second accumulator 572 accumulates the imaginary-partsymbols Y₀^(I), Y₁^(I),  …  , Y_(rN − 1)^(I)

[0062] and outputs an imaginary-part sequence .C₀^(I), C₁^(I),  …  , C_(rN − 1)^(I).

[0063] Instead of the accumulators 570 and 572, one-tap or two-tap RSCcoders can be used.

[0064] The accumulated symbols are input to a signal mapper 580. Thesignal mapper 580 determines a signal s_(ij) to be transmitted through aj^(th) antenna at an i^(th) time by mapping accumulated symbols (C_(i)^(R),C_(i) ¹) in a signal constellation. A signal transmitted through aj^(th) antenna is s_(0j), s_(1j), . . . , s_(rN−1j) and the number oftransmission antennas 590 to 594 is equal to the repetition factor. Ifthe repetition factor is m, m antennas are used.

[0065] The receiver receives signals from the m antennas. If thereceived signals are expressed as R₀, R₁, . . . , _(RN) _(⁻) ₁, the loglikelihood of each component of (C_(i) ^(R),C_(i) ¹) in R_(i) iscalculated and an initial LLR (Log Likelihood Ratio) of a correspondingsymbol Z_(i) ^((k)) is calculated using the log likelihoods. Using theinitial LLR, Z_(i)^((k))

[0066] is decoded to U₀^((k)), U₁^((k)), …  , U_(N − 1)^((k))

[0067] by iterative decoding of concatenated codes through a combiner, aweighter, a deinterleaver, and an accumulator.

[0068] In accordance with the present invention, non-binary code symbolshave full rank like binary code symbols so that a receiver can receivetransmission data without errors. N symbols are repeated by a repetitionfactor r. The rN repeated symbols are weighted using weighting factorsother than zero and thus randomized. Therefore, the performance ofchannel encoding is improved.

[0069] Each of the rN weighted symbols is converted to m bits. The mbits are assigned to m antennas, respectively. To obtain a maximum datarate, r is set to m. Thus, a maximum diversity gain is achievedirrespective of the type of the interleaver.

[0070] While the invention has been shown and described with referenceto certain preferred embodiments thereof, it will be understood by thoseskilled in the art that various changes in form and details may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims.

What is claimed is:
 1. A mobile communication system using multipleantennas comprising: a repeater for receiving non-binary symbols andrepeating the non-binary symbols wherein a plurality of binary bits arerepresented by a non-binary element; a weighter for multiplying therepeated non-binary symbols by a corresponding weighting factor; aninterleaver for interleaving the weighted non-binary symbols; and acoder for coding the interleaved symbols.
 2. The mobile communicationsystem of claim 1, further comprising a mapper for mapping the pluralityof binary bits to the non-binary element over a Galois Field, GF2^(m),where m is the number of binary bits mapped to a non-binary element. 3.The mobile communication system of claim 1, wherein the weighter has thenon-binary elements over a Galois Field, GF2^(m), as the weightingfactors.
 4. The mobile communication system of claim 3, wherein theweighter has a number of weighting factors equal to a number of therepetition and multiplies the same repeated symbols by the differentweighting factors.
 5. The mobile communication system of claim 1,wherein the coder comprises an accumulator.
 6. The mobile communicationsystem of claim 1, wherein the coder comprises a Recursive SystematicConvolutional code (RSC).
 7. The mobile communication system of claim 5,wherein the coder comprises an accumulator for receiving said non-binarysymbols from the interleaver and sequentially accumulating thenon-binary symbols.
 8. The mobile communication system of claim 6,wherein the coder comprises an 1 tap Recursive Systematic Convolutionalcode (RSC).
 9. The mobile communication system of claim 1, furthercomprising a demapper for mapping the encoded symbols to a plurality ofbinary bits.
 10. The mobile communication system of claim 9, furthercomprising a signal mapper for assigning the plurality of binary symbolsreceived from the demapper to the antennas respectively.
 11. A mobilecommunication system using multiple antennas comprising the steps of:receiving non-binary symbols and repeating the non-binary symbols of asymbols wherein a plurality of binary bits are represented by anon-binary element; multiplying the repeated non-binary symbols by acorresponding weighting factor; interleaving the weighted non-binarysymbols; and coding the interleaved symbols.
 12. The mobilecommunication system of claim 1 1, further comprising the step ofmapping the plurality of binary bits to the non-binary element over aGalois Field, GF2^(m), where m is the number of binary bits mapped to anon-binary element.
 13. The mobile communication system of claim 11,wherein the weighting factors are the non-binary elements of a GaloisField, GF2^(m).
 14. The mobile communication system of claim 11, whereina number of weighting factors are equal to a number of the repetitionand the same repeated symbols are multiplied by the different weightingfactors.
 15. The mobile communication system of claim 11, wherein thecoding is performed by Recursive Systematic Convolutional coding (RSC)the interleaved non-binary symbols.
 16. The mobile communication systemof claim 1, wherein the coding is performed by sequentially accumulatingthe interleaved non-binary symbols.
 17. The mobile communication systemof claim 15, wherein the Recursive Systematic Convolutional coding (RSC)is a 1 tap Recursive Systematic Convolutional coding (RSC).
 18. Themobile communication system of claim 11, further comprising the step ofmapping the encoded non-binary symbols to a plurality of binary bits.19. The mobile communication system of claim 11, further comprising thestep of assigning the plurality of binary symbols to respectiveantennas.
 20. The mobile communication system of claim 14, wherein theweighting factors are GF2^(m) elements other than zero.